Wonder if that works if you cast it it for free? It still has an x in it's cost and it has a value for x, but I'm really not sure what would happen.

You'd make a 0/0 Hydra token, the token will immediately die, and then nothing else happens.

It is true that if you cast most x cost spells for free, x must be 0 and thus you make a 0/0 with no counters. Shoals are an exception to that and to the best of my knowledge, they should give you size equal to x.

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"Hail to the speaker, hail to the knower; joy to he who has understood, delight to they who have listened." - Odin

With Doubling Season, you can still only put counters on one of the created tokens, right?

Good question actually. You should be able to put counters on both tokens though. If you copy a creature with Kiki-Jiki, Mirror Breaker with Doubling Season out, you will have to sacrifice both tokens at end of turn, because they were created by the same effect. The same should apply here. Amass cards like Commence the Endgame are different, because the counters are not directly related to the created token.